MinT - Best Known (130−31, 130, s)-Nets in Base 4

Best Known (130−31, 130, s)-Nets in Base 4

(130−31, 130, 1032)-Net over F₄ — Constructive and digital

Digital (99, 130, 1032)-net over F₄, using

4² 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]

(130−31, 130, 1646)-Net over F₄ — Digital

Digital (99, 130, 1646)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−31, 130, 322362)-Net in Base 4 — Upper bound on s

There is no (99, 130, 322363)-net in base 4, because

1 times m-reduction [i] would yield (99, 129, 322363)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 463169 052344 737312 408509 679886 462534 016270 153095 684160 599590 058875 684656 791200 > 4¹²⁹ [i]