MinT - Best Known (93, 93+79, s)-Nets in Base 4

Best Known (93, 93+79, s)-Nets in Base 4

(93, 93+79, 130)-Net over F₄ — Constructive and digital

Digital (93, 172, 130)-net over F₄, using

2 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+79, 165)-Net over F₄ — Digital

Digital (93, 172, 165)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(93, 93+79, 2207)-Net in Base 4 — Upper bound on s

There is no (93, 172, 2208)-net in base 4, because

1 times m-reduction [i] would yield (93, 171, 2208)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 046925 071244 965154 311645 636010 089128 809654 512155 244399 428536 657379 159365 375023 152588 329859 243624 801220 > 4¹⁷¹ [i]