MinT - Best Known (129−31, 129, s)-Nets in Base 4

Best Known (129−31, 129, s)-Nets in Base 4

(129−31, 129, 1032)-Net over F₄ — Constructive and digital

Digital (98, 129, 1032)-net over F₄, using

4¹ times duplication [i] based on digital (97, 128, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 32, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(129−31, 129, 1573)-Net over F₄ — Digital

Digital (98, 129, 1573)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−31, 129, 293904)-Net in Base 4 — Upper bound on s

There is no (98, 129, 293905)-net in base 4, because

1 times m-reduction [i] would yield (98, 128, 293905)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 115794 997528 688644 701808 746682 187478 484443 121303 165698 414274 945264 618107 185104 > 4¹²⁸ [i]