MinT - Best Known (132−31, 132, s)-Nets in Base 4

Best Known (132−31, 132, s)-Nets in Base 4

(132−31, 132, 1036)-Net over F₄ — Constructive and digital

Digital (101, 132, 1036)-net over F₄, using

trace code for nets [i] based on digital (2, 33, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(132−31, 132, 1804)-Net over F₄ — Digital

Digital (101, 132, 1804)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−31, 132, 387813)-Net in Base 4 — Upper bound on s

There is no (101, 132, 387814)-net in base 4, because

1 times m-reduction [i] would yield (101, 131, 387814)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7 410935 304237 373870 268413 943000 153610 387504 851424 664261 421128 233866 941071 135760 > 4¹³¹ [i]