MinT - Best Known (11, 11+62, s)-Nets in Base 81

Best Known (11, 11+62, s)-Nets in Base 81

(11, 11+62, 172)-Net over F₈₁ — Constructive and digital

Digital (11, 73, 172)-net over F₈₁, using

t-expansion [i] based on digital (7, 73, 172)-net over F₈₁, using
- net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
    - a function field by SÃ©mirat [i]

(11, 11+62, 244)-Net over F₈₁ — Digital

Digital (11, 73, 244)-net over F₈₁, using

t-expansion [i] based on digital (9, 73, 244)-net over F₈₁, using
- net from sequence [i] based on digital (9, 243)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 9 and N(F) ≥ 244, using
    - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₈₁ [i]

(11, 11+62, 4827)-Net in Base 81 — Upper bound on s

There is no (11, 73, 4828)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 20 910634 696507 197609 405696 447606 482497 097618 242160 812616 189279 584740 974753 164046 294493 751234 845465 767505 939114 179199 457089 527393 406788 229441 > 81⁷³ [i]