MinT - Best Known (236−57, 236, s)-Nets in Base 4

Best Known (236−57, 236, s)-Nets in Base 4

(236−57, 236, 1036)-Net over F₄ — Constructive and digital

Digital (179, 236, 1036)-net over F₄, using

trace code for nets [i] based on digital (2, 59, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(236−57, 236, 2521)-Net over F₄ — Digital

Digital (179, 236, 2521)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−57, 236, 425465)-Net in Base 4 — Upper bound on s

There is no (179, 236, 425466)-net in base 4, because

1 times m-reduction [i] would yield (179, 235, 425466)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3048 758098 235370 668819 216771 068266 723985 213030 653444 734239 764334 661749 186885 844441 035047 528787 438346 245780 338864 995007 806665 881012 677236 191112 > 4²³⁵ [i]