MinT - Best Known (135, 135+40, s)-Nets in Base 4

Best Known (135, 135+40, s)-Nets in Base 4

(135, 135+40, 1040)-Net over F₄ — Constructive and digital

Digital (135, 175, 1040)-net over F₄, using

1 times m-reduction [i] based on digital (135, 176, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 44, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(135, 135+40, 2601)-Net over F₄ — Digital

Digital (135, 175, 2601)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(135, 135+40, 513093)-Net in Base 4 — Upper bound on s

There is no (135, 175, 513094)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2293 574595 469550 627703 943867 667444 287207 109286 304526 152859 577765 351704 967120 326330 410255 820572 759220 902204 > 4¹⁷⁵ [i]