MinT - Best Known (87−70, 87, s)-Nets in Base 64

Best Known (87−70, 87, s)-Nets in Base 64

(87−70, 87, 177)-Net over F₆₄ — Constructive and digital

Digital (17, 87, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 87, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(87−70, 87, 192)-Net in Base 64 — Constructive

(17, 87, 192)-net in base 64, using

t-expansion [i] based on (16, 87, 192)-net in base 64, using
- 4 times m-reduction [i] based on (16, 91, 192)-net in base 64, using
  - base change [i] based on digital (3, 78, 192)-net over F₁₂₈, using
    - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(87−70, 87, 267)-Net over F₆₄ — Digital

Digital (17, 87, 267)-net over F₆₄, using

t-expansion [i] based on digital (16, 87, 267)-net over F₆₄, using
- net from sequence [i] based on digital (16, 266)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 16 and N(F) ≥ 267, using
    - a curve from the manYPoints database [i]

(87−70, 87, 6799)-Net in Base 64 — Upper bound on s

There is no (17, 87, 6800)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 13 793382 158157 882671 091918 567283 867601 995881 617993 262522 597160 524016 122015 507058 093217 123439 662199 443454 085569 280570 036589 929110 325864 172559 197062 049090 307292 > 64⁸⁷ [i]