MinT - Best Known (71−52, 71, s)-Nets in Base 64

Best Known (71−52, 71, s)-Nets in Base 64

(71−52, 71, 177)-Net over F₆₄ — Constructive and digital

Digital (19, 71, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 71, 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]

(71−52, 71, 258)-Net in Base 64 — Constructive

(19, 71, 258)-net in base 64, using

1 times m-reduction [i] based on (19, 72, 258)-net in base 64, using
- base change [i] based on digital (1, 54, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(71−52, 71, 315)-Net over F₆₄ — Digital

Digital (19, 71, 315)-net over F₆₄, using

net from sequence [i] based on digital (19, 314)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 19 and N(F) ≥ 315, using
  - a curve from the manYPoints database [i]

(71−52, 71, 14316)-Net in Base 64 — Upper bound on s

There is no (19, 71, 14317)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 173 606340 773201 054353 682459 143539 197736 926705 315167 949249 099159 557031 247227 471813 685010 523129 334278 451959 863178 006318 848063 564540 > 64⁷¹ [i]