MinT - Best Known (177−41, 177, s)-Nets in Base 4

Best Known (177−41, 177, s)-Nets in Base 4

(177−41, 177, 1040)-Net over F₄ — Constructive and digital

Digital (136, 177, 1040)-net over F₄, using

4¹ times duplication [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]

(177−41, 177, 2445)-Net over F₄ — Digital

Digital (136, 177, 2445)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−41, 177, 549920)-Net in Base 4 — Upper bound on s

There is no (136, 177, 549921)-net in base 4, because

1 times m-reduction [i] would yield (136, 176, 549921)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9174 067067 140920 740170 048260 646414 769801 771951 815719 761974 388608 064690 707619 384654 879982 816211 872338 932936 > 4¹⁷⁶ [i]