MinT - Best Known (259−51, 259, s)-Nets in Base 4

Best Known (259−51, 259, s)-Nets in Base 4

(259−51, 259, 1539)-Net over F₄ — Constructive and digital

Digital (208, 259, 1539)-net over F₄, using

4¹ times duplication [i] based on digital (207, 258, 1539)-net over F₄, using
- t-expansion [i] based on digital (200, 258, 1539)-net over F₄, using
  - trace code for nets [i] based on digital (28, 86, 513)-net over F₆₄, using
    - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(259−51, 259, 8560)-Net over F₄ — Digital

Digital (208, 259, 8560)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(259−51, 259, 5543219)-Net in Base 4 — Upper bound on s

There is no (208, 259, 5543220)-net in base 4, because

1 times m-reduction [i] would yield (208, 258, 5543220)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 214525 240286 815049 707535 393615 414181 775895 718869 260091 191622 351737 243078 082396 910590 674845 487631 145282 354571 367070 047753 080966 878127 632704 505022 013292 416668 > 4²⁵⁸ [i]