MinT - Best Known (172−78, 172, s)-Nets in Base 4

Best Known (172−78, 172, s)-Nets in Base 4

(172−78, 172, 130)-Net over F₄ — Constructive and digital

Digital (94, 172, 130)-net over F₄, using

4 times m-reduction [i] based on digital (94, 176, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 88, 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]

(172−78, 172, 171)-Net over F₄ — Digital

Digital (94, 172, 171)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−78, 172, 2288)-Net in Base 4 — Upper bound on s

There is no (94, 172, 2289)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 36 161685 492382 096462 794131 266218 093324 912655 239267 624966 478528 620831 418553 375740 541463 073775 473125 618544 > 4¹⁷² [i]