MinT - Best Known (170−67, 170, s)-Nets in Base 4

Best Known (170−67, 170, s)-Nets in Base 4

(170−67, 170, 130)-Net over F₄ — Constructive and digital

Digital (103, 170, 130)-net over F₄, using

24 times m-reduction [i] based on digital (103, 194, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 97, 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]

(170−67, 170, 267)-Net over F₄ — Digital

Digital (103, 170, 267)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−67, 170, 5288)-Net in Base 4 — Upper bound on s

There is no (103, 170, 5289)-net in base 4, because

1 times m-reduction [i] would yield (103, 169, 5289)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 562960 839951 989297 677043 824218 077388 301752 302499 705196 104117 906911 849080 302639 953374 992535 743857 552380 > 4¹⁶⁹ [i]