MinT - Best Known (240−135, 240, s)-Nets in Base 4

Best Known (240−135, 240, s)-Nets in Base 4

(240−135, 240, 130)-Net over F₄ — Constructive and digital

Digital (105, 240, 130)-net over F₄, using

net from sequence [i] based on digital (105, 129)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
  - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(240−135, 240, 144)-Net over F₄ — Digital

Digital (105, 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]

(240−135, 240, 1153)-Net in Base 4 — Upper bound on s

There is no (105, 240, 1154)-net in base 4, because

1 times m-reduction [i] would yield (105, 239, 1154)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 818502 253374 642361 227496 805809 233484 058397 890371 883918 137723 627755 317690 232137 667147 188425 765071 141693 157399 280637 155713 252437 799518 185757 575200 > 4²³⁹ [i]