MinT - Best Known (177−43, 177, s)-Nets in Base 4

Best Known (177−43, 177, s)-Nets in Base 4

(177−43, 177, 1032)-Net over F₄ — Constructive and digital

Digital (134, 177, 1032)-net over F₄, using

4¹ times duplication [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]

(177−43, 177, 1917)-Net over F₄ — Digital

Digital (134, 177, 1917)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−43, 177, 321502)-Net in Base 4 — Upper bound on s

There is no (134, 177, 321503)-net in base 4, because

1 times m-reduction [i] would yield (134, 176, 321503)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9174 243957 376438 478766 236405 196145 624801 534222 984212 478570 992424 599439 766031 902010 743065 317051 668424 987790 > 4¹⁷⁶ [i]