MinT - Best Known (239−57, 239, s)-Nets in Base 4

Best Known (239−57, 239, s)-Nets in Base 4

(239−57, 239, 1036)-Net over F₄ — Constructive and digital

Digital (182, 239, 1036)-net over F₄, using

1 times m-reduction [i] based on digital (182, 240, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 60, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(239−57, 239, 2713)-Net over F₄ — Digital

Digital (182, 239, 2713)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(239−57, 239, 493598)-Net in Base 4 — Upper bound on s

There is no (182, 239, 493599)-net in base 4, because

1 times m-reduction [i] would yield (182, 238, 493599)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 195117 579119 157455 717718 758559 577616 493972 864310 201104 416673 775123 485247 740511 992482 659925 960752 215287 943077 933116 615608 217464 958295 292293 760931 > 4²³⁸ [i]