MinT - Best Known (93, 93+75, s)-Nets in Base 4

Best Known (93, 93+75, s)-Nets in Base 4

(93, 93+75, 130)-Net over F₄ — Constructive and digital

Digital (93, 168, 130)-net over F₄, using

6 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, 93+75, 177)-Net over F₄ — Digital

Digital (93, 168, 177)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(93, 93+75, 2517)-Net in Base 4 — Upper bound on s

There is no (93, 168, 2518)-net in base 4, because

1 times m-reduction [i] would yield (93, 167, 2518)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35104 454854 923255 880791 695986 107312 441938 674338 510122 405787 250716 153198 588765 891736 984716 064278 102250 > 4¹⁶⁷ [i]