MinT - Best Known (202−47, 202, s)-Nets in Base 4

Best Known (202−47, 202, s)-Nets in Base 4

(202−47, 202, 1040)-Net over F₄ — Constructive and digital

Digital (155, 202, 1040)-net over F₄, using

4² times duplication [i] based on digital (153, 200, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 50, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(202−47, 202, 2665)-Net over F₄ — Digital

Digital (155, 202, 2665)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(202−47, 202, 573854)-Net in Base 4 — Upper bound on s

There is no (155, 202, 573855)-net in base 4, because

1 times m-reduction [i] would yield (155, 201, 573855)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 329260 992752 542458 090917 250226 814872 176228 541967 624818 255155 856013 129753 193493 596108 916818 215784 347380 236522 180690 212436 > 4²⁰¹ [i]