MinT - Best Known (252−157, 252, s)-Nets in Base 4

Best Known (252−157, 252, s)-Nets in Base 4

(252−157, 252, 104)-Net over F₄ — Constructive and digital

Digital (95, 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]

(252−157, 252, 144)-Net over F₄ — Digital

Digital (95, 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]

(252−157, 252, 798)-Net in Base 4 — Upper bound on s

There is no (95, 252, 799)-net in base 4, because

1 times m-reduction [i] would yield (95, 251, 799)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 192197 962585 545591 398776 786968 296120 715899 661623 380263 535403 550534 455143 783137 646503 792576 493452 730539 328785 625311 237600 762422 579627 268882 383139 849036 > 4²⁵¹ [i]