MinT - Best Known (243−140, 243, s)-Nets in Base 4

Best Known (243−140, 243, s)-Nets in Base 4

(243−140, 243, 104)-Net over F₄ — Constructive and digital

Digital (103, 243, 104)-net over F₄, using

t-expansion [i] based on digital (73, 243, 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]

(243−140, 243, 144)-Net over F₄ — Digital

Digital (103, 243, 144)-net over F₄, using

t-expansion [i] based on digital (91, 243, 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]

(243−140, 243, 1046)-Net in Base 4 — Upper bound on s

There is no (103, 243, 1047)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 208 864704 243211 929668 069859 577481 688518 501754 405542 322317 936338 757722 530842 530119 913210 244372 368391 541638 402413 446236 108692 991836 421927 421377 280880 > 4²⁴³ [i]