MinT - Best Known (252−156, 252, s)-Nets in Base 4

Best Known (252−156, 252, s)-Nets in Base 4

(252−156, 252, 104)-Net over F₄ — Constructive and digital

Digital (96, 252, 104)-net over F₄, using

t-expansion [i] based on digital (73, 252, 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]

(252−156, 252, 144)-Net over F₄ — Digital

Digital (96, 252, 144)-net over F₄, using

t-expansion [i] based on digital (91, 252, 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]

(252−156, 252, 814)-Net in Base 4 — Upper bound on s

There is no (96, 252, 815)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 55 554716 343691 583046 819338 221020 721007 099733 633426 572882 699649 043087 649251 150715 844391 030137 115781 301417 737693 609330 901057 749828 141170 454002 689301 703500 > 4²⁵² [i]