MinT - Best Known (158−60, 158, s)-Nets in Base 4

Best Known (158−60, 158, s)-Nets in Base 4

(158−60, 158, 130)-Net over F₄ — Constructive and digital

Digital (98, 158, 130)-net over F₄, using

26 times m-reduction [i] based on digital (98, 184, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 92, 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]

(158−60, 158, 285)-Net over F₄ — Digital

Digital (98, 158, 285)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(158−60, 158, 5925)-Net in Base 4 — Upper bound on s

There is no (98, 158, 5926)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 133812 478625 785306 609991 152752 116189 220256 050814 669692 076690 423478 959519 106476 213171 633854 378640 > 4¹⁵⁸ [i]