MinT - Best Known (168, 168+42, s)-Nets in Base 4

Best Known (168, 168+42, s)-Nets in Base 4

(168, 168+42, 1539)-Net over F₄ — Constructive and digital

Digital (168, 210, 1539)-net over F₄, using

trace code for nets [i] based on digital (28, 70, 513)-net over F₆₄, using
- net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
    - the Hermitian function field over F₆₄ [i]

(168, 168+42, 6544)-Net over F₄ — Digital

Digital (168, 210, 6544)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(168, 168+42, 3033673)-Net in Base 4 — Upper bound on s

There is no (168, 210, 3033674)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 707700 614845 650725 178953 636344 952969 879215 373179 806847 332721 648145 803259 754156 465709 753272 190921 447563 300505 551845 284356 591608 > 4²¹⁰ [i]