MinT - Best Known (97, 97+30, s)-Nets in Base 4

Best Known (97, 97+30, s)-Nets in Base 4

(97, 97+30, 1032)-Net over F₄ — Constructive and digital

Digital (97, 127, 1032)-net over F₄, using

1 times m-reduction [i] based on digital (97, 128, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 32, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(97, 97+30, 1699)-Net over F₄ — Digital

Digital (97, 127, 1699)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(97, 97+30, 267958)-Net in Base 4 — Upper bound on s

There is no (97, 127, 267959)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 28949 172798 923725 703743 261124 209021 986318 662502 104860 489263 499415 936541 645688 > 4¹²⁷ [i]