MinT - Best Known (79−64, 79, s)-Nets in Base 64

Best Known (79−64, 79, s)-Nets in Base 64

(79−64, 79, 177)-Net over F₆₄ — Constructive and digital

Digital (15, 79, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 79, 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]

(79−64, 79, 192)-Net in Base 64 — Constructive

(15, 79, 192)-net in base 64, using

5 times m-reduction [i] based on (15, 84, 192)-net in base 64, using
- base change [i] based on digital (3, 72, 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]

(79−64, 79, 258)-Net over F₆₄ — Digital

Digital (15, 79, 258)-net over F₆₄, using

net from sequence [i] based on digital (15, 257)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 15 and N(F) ≥ 258, using
  - a curve from the manYPoints database [i]

(79−64, 79, 5825)-Net in Base 64 — Upper bound on s

There is no (15, 79, 5826)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 48830 794636 829113 721733 076058 331768 924761 580283 791474 898004 049094 476541 422152 864942 597789 282595 597783 719047 800494 826492 743022 484611 074104 000402 > 64⁷⁹ [i]