MinT - Best Known (137, 137+42, s)-Nets in Base 4

Best Known (137, 137+42, s)-Nets in Base 4

(137, 137+42, 1036)-Net over F₄ — Constructive and digital

Digital (137, 179, 1036)-net over F₄, using

1 times m-reduction [i] based on digital (137, 180, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 45, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(137, 137+42, 2307)-Net over F₄ — Digital

Digital (137, 179, 2307)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 137+42, 391919)-Net in Base 4 — Upper bound on s

There is no (137, 179, 391920)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 587143 120458 094451 455277 827473 521459 242209 977686 594272 640456 043014 058596 882460 618238 327813 369176 134919 973694 > 4¹⁷⁹ [i]