MinT - Best Known (218−126, 218, s)-Nets in Base 4

Best Known (218−126, 218, s)-Nets in Base 4

(218−126, 218, 104)-Net over F₄ — Constructive and digital

Digital (92, 218, 104)-net over F₄, using

t-expansion [i] based on digital (73, 218, 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]

(218−126, 218, 144)-Net over F₄ — Digital

Digital (92, 218, 144)-net over F₄, using

t-expansion [i] based on digital (91, 218, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(218−126, 218, 930)-Net in Base 4 — Upper bound on s

There is no (92, 218, 931)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 183559 787204 251232 180393 632115 495924 785501 104159 078514 764631 723535 231812 328307 475091 775734 735103 663963 349444 602954 167091 765562 155520 > 4²¹⁸ [i]