MinT - Best Known (29, 77, s)-Nets in Base 81

Best Known (29, 77, s)-Nets in Base 81

(29, 77, 370)-Net over F₈₁ — Constructive and digital

Digital (29, 77, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 77, 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, 77, 500)-Net over F₈₁ — Digital

Digital (29, 77, 500)-net over F₈₁, using

t-expansion [i] based on digital (26, 77, 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, 77, 162666)-Net in Base 81 — Upper bound on s

There is no (29, 77, 162667)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 898 249638 198674 553022 957891 098035 160048 938000 710544 999521 554288 176257 263476 875763 007066 249350 710202 643541 340462 894058 838651 430582 347050 898841 651841 > 81⁷⁷ [i]