MinT - Best Known (221−142, 221, s)-Nets in Base 4

Best Known (221−142, 221, s)-Nets in Base 4

(221−142, 221, 104)-Net over F₄ — Constructive and digital

Digital (79, 221, 104)-net over F₄, using

t-expansion [i] based on digital (73, 221, 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]

(221−142, 221, 112)-Net over F₄ — Digital

Digital (79, 221, 112)-net over F₄, using

t-expansion [i] based on digital (73, 221, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(221−142, 221, 623)-Net in Base 4 — Upper bound on s

There is no (79, 221, 624)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 338330 827235 260973 998259 835068 344957 744586 710712 759936 263823 648487 149272 309139 508698 463903 758341 025394 998563 058733 501922 432197 738763 > 4²²¹ [i]