MinT - Best Known (138−94, 138, s)-Nets in Base 9

Best Known (138−94, 138, s)-Nets in Base 9

(138−94, 138, 81)-Net over F₉ — Constructive and digital

Digital (44, 138, 81)-net over F₉, using

t-expansion [i] based on digital (32, 138, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(138−94, 138, 147)-Net over F₉ — Digital

Digital (44, 138, 147)-net over F₉, using

t-expansion [i] based on digital (43, 138, 147)-net over F₉, using
- net from sequence [i] based on digital (43, 146)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
    - a curve from the manYPoints database [i]

(138−94, 138, 1426)-Net in Base 9 — Upper bound on s

There is no (44, 138, 1427)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 497808 392667 349531 721786 758193 099938 848289 288116 864774 211256 747407 777756 771146 589133 876556 492977 938263 779123 080928 530478 734249 394025 > 9¹³⁸ [i]