MinT - Best Known (146−67, 146, s)-Nets in Base 4

Best Known (146−67, 146, s)-Nets in Base 4

(146−67, 146, 130)-Net over F₄ — Constructive and digital

Digital (79, 146, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 73, 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]

(146−67, 146, 144)-Net over F₄ — Digital

Digital (79, 146, 144)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−67, 146, 1912)-Net in Base 4 — Upper bound on s

There is no (79, 146, 1913)-net in base 4, because

1 times m-reduction [i] would yield (79, 145, 1913)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2007 771500 574000 011799 192408 704617 287391 273970 267583 252514 386049 510616 859931 476843 254140 > 4¹⁴⁵ [i]