MinT - Best Known (211−43, 211, s)-Nets in Base 4

Best Known (211−43, 211, s)-Nets in Base 4

(211−43, 211, 1064)-Net over F₄ — Constructive and digital

Digital (168, 211, 1064)-net over F₄, using

1 times m-reduction [i] based on digital (168, 212, 1064)-net over F₄, using
- trace code for nets [i] based on digital (9, 53, 266)-net over F₂₅₆, using
  - net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(211−43, 211, 5846)-Net over F₄ — Digital

Digital (168, 211, 5846)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−43, 211, 3033673)-Net in Base 4 — Upper bound on s

There is no (168, 211, 3033674)-net in base 4, because

1 times m-reduction [i] would yield (168, 210, 3033674)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 707700 614845 650725 178953 636344 952969 879215 373179 806847 332721 648145 803259 754156 465709 753272 190921 447563 300505 551845 284356 591608 > 4²¹⁰ [i]