MinT - Best Known (93, 159, s)-Nets in Base 4

Best Known (93, 159, s)-Nets in Base 4

(93, 159, 130)-Net over F₄ — Constructive and digital

Digital (93, 159, 130)-net over F₄, using

15 times m-reduction [i] based on digital (93, 174, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 87, 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]

(93, 159, 212)-Net over F₄ — Digital

Digital (93, 159, 212)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(93, 159, 3465)-Net in Base 4 — Upper bound on s

There is no (93, 159, 3466)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 538941 325901 046749 713705 380737 354430 679684 802094 961596 584668 008451 000437 440808 904958 623553 050396 > 4¹⁵⁹ [i]