MinT - Best Known (178−75, 178, s)-Nets in Base 4

Best Known (178−75, 178, s)-Nets in Base 4

(178−75, 178, 130)-Net over F₄ — Constructive and digital

Digital (103, 178, 130)-net over F₄, using

16 times m-reduction [i] based on digital (103, 194, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 97, 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]

(178−75, 178, 223)-Net over F₄ — Digital

Digital (103, 178, 223)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−75, 178, 3675)-Net in Base 4 — Upper bound on s

There is no (103, 178, 3676)-net in base 4, because

1 times m-reduction [i] would yield (103, 177, 3676)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 36752 256304 017158 392407 112046 419964 360437 356854 897736 292220 763571 642130 544621 942102 639767 781753 613154 001580 > 4¹⁷⁷ [i]