MinT - Best Known (123−84, 123, s)-Nets in Base 9

Best Known (123−84, 123, s)-Nets in Base 9

(123−84, 123, 81)-Net over F₉ — Constructive and digital

Digital (39, 123, 81)-net over F₉, using

t-expansion [i] based on digital (32, 123, 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]

(123−84, 123, 140)-Net over F₉ — Digital

Digital (39, 123, 140)-net over F₉, using

net from sequence [i] based on digital (39, 139)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 39 and N(F) ≥ 140, using
  - a curve from the manYPoints database [i]

(123−84, 123, 1260)-Net in Base 9 — Upper bound on s

There is no (39, 123, 1261)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2391 829161 138071 399710 942977 504102 869571 007544 517246 127896 977013 318146 184394 367687 975139 343590 308040 667872 108247 707345 > 9¹²³ [i]