MinT - Best Known (129−30, 129, s)-Nets in Base 4

Best Known (129−30, 129, s)-Nets in Base 4

(129−30, 129, 1036)-Net over F₄ — Constructive and digital

Digital (99, 129, 1036)-net over F₄, using

4¹ times duplication [i] based on digital (98, 128, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 32, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(129−30, 129, 1868)-Net over F₄ — Digital

Digital (99, 129, 1868)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−30, 129, 322362)-Net in Base 4 — Upper bound on s

There is no (99, 129, 322363)-net in base 4, because

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]