MinT - Best Known (256−59, 256, s)-Nets in Base 4

Best Known (256−59, 256, s)-Nets in Base 4

(256−59, 256, 1048)-Net over F₄ — Constructive and digital

Digital (197, 256, 1048)-net over F₄, using

trace code for nets [i] based on digital (5, 64, 262)-net over F₂₅₆, using
- net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(256−59, 256, 3429)-Net over F₄ — Digital

Digital (197, 256, 3429)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(256−59, 256, 765531)-Net in Base 4 — Upper bound on s

There is no (197, 256, 765532)-net in base 4, because

1 times m-reduction [i] would yield (197, 255, 765532)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3352 000321 092273 163734 115730 866778 539588 372044 934479 640171 033836 563085 270416 908272 940494 527509 688506 850154 189014 905100 478100 039979 102695 797709 306514 320528 > 4²⁵⁵ [i]