MinT - Best Known (42, 42+78, s)-Nets in Base 9

Best Known (42, 42+78, s)-Nets in Base 9

(42, 42+78, 81)-Net over F₉ — Constructive and digital

Digital (42, 120, 81)-net over F₉, using

t-expansion [i] based on digital (32, 120, 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]

(42, 42+78, 140)-Net over F₉ — Digital

Digital (42, 120, 140)-net over F₉, using

t-expansion [i] based on digital (39, 120, 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]

(42, 42+78, 1637)-Net in Base 9 — Upper bound on s

There is no (42, 120, 1638)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 260157 323335 820468 077389 986248 118557 563381 338920 966273 874716 774768 839753 745542 637450 326230 309131 878263 986260 081297 > 9¹²⁰ [i]