MinT - Best Known (89, 89+27, s)-Nets in Base 4

Best Known (89, 89+27, s)-Nets in Base 4

(89, 89+27, 1036)-Net over F₄ — Constructive and digital

Digital (89, 116, 1036)-net over F₄, using

trace code for nets [i] based on digital (2, 29, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(89, 89+27, 1720)-Net over F₄ — Digital

Digital (89, 116, 1720)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 89+27, 400118)-Net in Base 4 — Upper bound on s

There is no (89, 116, 400119)-net in base 4, because

1 times m-reduction [i] would yield (89, 115, 400119)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1725 444800 664673 802918 153022 693376 394902 116383 610974 205634 648905 907300 > 4¹¹⁵ [i]