MinT - Best Known (83, 154, s)-Nets in Base 4

Best Known (83, 154, s)-Nets in Base 4

(83, 154, 130)-Net over F₄ — Constructive and digital

Digital (83, 154, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 77, 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]

(83, 154, 148)-Net over F₄ — Digital

Digital (83, 154, 148)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 154, 1957)-Net in Base 4 — Upper bound on s

There is no (83, 154, 1958)-net in base 4, because

1 times m-reduction [i] would yield (83, 153, 1958)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 131 274603 307718 535003 800336 276543 630076 139040 720661 328625 993451 054470 647148 694999 540710 451070 > 4¹⁵³ [i]