MinT - Best Known (59, 59+45, s)-Nets in Base 4

Best Known (59, 59+45, s)-Nets in Base 4

(59, 59+45, 130)-Net over F₄ — Constructive and digital

Digital (59, 104, 130)-net over F₄, using

2 times m-reduction [i] based on digital (59, 106, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 53, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(59, 59+45, 131)-Net over F₄ — Digital

Digital (59, 104, 131)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+45, 1970)-Net in Base 4 — Upper bound on s

There is no (59, 104, 1971)-net in base 4, because

1 times m-reduction [i] would yield (59, 103, 1971)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 103 459494 418836 665654 424578 700401 342083 788693 865286 668560 572536 > 4¹⁰³ [i]