MinT - Best Known (147−59, 147, s)-Nets in Base 4

Best Known (147−59, 147, s)-Nets in Base 4

(147−59, 147, 130)-Net over F₄ — Constructive and digital

Digital (88, 147, 130)-net over F₄, using

17 times m-reduction [i] based on digital (88, 164, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 82, 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]

(147−59, 147, 222)-Net over F₄ — Digital

Digital (88, 147, 222)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−59, 147, 4155)-Net in Base 4 — Upper bound on s

There is no (88, 147, 4156)-net in base 4, because

1 times m-reduction [i] would yield (88, 146, 4156)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7997 062457 339361 311262 165214 865553 062302 683613 158532 429005 712105 233444 068126 581220 004712 > 4¹⁴⁶ [i]