MinT - Best Known (29, 29+46, s)-Nets in Base 81

Best Known (29, 29+46, s)-Nets in Base 81

(29, 29+46, 370)-Net over F₈₁ — Constructive and digital

Digital (29, 75, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 75, 370)-net over F₈₁, using
- net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]

(29, 29+46, 500)-Net over F₈₁ — Digital

Digital (29, 75, 500)-net over F₈₁, using

t-expansion [i] based on digital (26, 75, 500)-net over F₈₁, using
- net from sequence [i] based on digital (26, 499)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 26 and N(F) ≥ 500, using
    - a curve from the manYPoints database [i]

(29, 29+46, 197088)-Net in Base 81 — Upper bound on s

There is no (29, 75, 197089)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 136893 300487 877098 318218 352094 562781 635268 971149 906273 743672 476236 143047 896942 034582 650094 969603 508302 176784 350018 897328 324154 036406 726900 659761 > 81⁷⁵ [i]