MinT - Best Known (133, 133+42, s)-Nets in Base 4

Best Known (133, 133+42, s)-Nets in Base 4

(133, 133+42, 1032)-Net over F₄ — Constructive and digital

Digital (133, 175, 1032)-net over F₄, using

1 times m-reduction [i] based on digital (133, 176, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 44, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(133, 133+42, 2018)-Net over F₄ — Digital

Digital (133, 175, 2018)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(133, 133+42, 300963)-Net in Base 4 — Upper bound on s

There is no (133, 175, 300964)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2293 628745 463473 051037 422789 911093 693386 671432 443304 280607 346296 096593 169550 518581 408799 885083 239026 218168 > 4¹⁷⁵ [i]