MinT - Best Known (255−170, 255, s)-Nets in Base 4

Best Known (255−170, 255, s)-Nets in Base 4

(255−170, 255, 104)-Net over F₄ — Constructive and digital

Digital (85, 255, 104)-net over F₄, using

t-expansion [i] based on digital (73, 255, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(255−170, 255, 129)-Net over F₄ — Digital

Digital (85, 255, 129)-net over F₄, using

t-expansion [i] based on digital (81, 255, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(255−170, 255, 624)-Net in Base 4 — Upper bound on s

There is no (85, 255, 625)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3584 016302 240995 048468 476214 973782 364376 139443 839025 556703 748339 030178 423614 099783 656570 058299 027375 332536 979290 511409 948486 474656 342348 864290 101885 286976 > 4²⁵⁵ [i]