MinT - Best Known (88, 88+27, s)-Nets in Base 4

Best Known (88, 88+27, s)-Nets in Base 4

(88, 88+27, 1032)-Net over F₄ — Constructive and digital

Digital (88, 115, 1032)-net over F₄, using

1 times m-reduction [i] based on digital (88, 116, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 29, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(88, 88+27, 1631)-Net over F₄ — Digital

Digital (88, 115, 1631)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+27, 359646)-Net in Base 4 — Upper bound on s

There is no (88, 115, 359647)-net in base 4, because

1 times m-reduction [i] would yield (88, 114, 359647)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 431 371999 802797 219456 492893 376176 759289 901328 838425 217775 370232 670338 > 4¹¹⁴ [i]