MinT - Best Known (240−147, 240, s)-Nets in Base 4

Best Known (240−147, 240, s)-Nets in Base 4

(240−147, 240, 104)-Net over F₄ — Constructive and digital

Digital (93, 240, 104)-net over F₄, using

t-expansion [i] based on digital (73, 240, 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]

(240−147, 240, 144)-Net over F₄ — Digital

Digital (93, 240, 144)-net over F₄, using

t-expansion [i] based on digital (91, 240, 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]

(240−147, 240, 814)-Net in Base 4 — Upper bound on s

There is no (93, 240, 815)-net in base 4, because

1 times m-reduction [i] would yield (93, 239, 815)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 799064 177663 899418 615787 918087 164513 099398 551509 332285 559206 100658 950095 265342 386497 160553 056316 429155 320505 705931 622922 404071 445343 703625 040408 > 4²³⁹ [i]