MinT - Best Known (126−30, 126, s)-Nets in Base 4

Best Known (126−30, 126, s)-Nets in Base 4

(126−30, 126, 1032)-Net over F₄ — Constructive and digital

Digital (96, 126, 1032)-net over F₄, using

4² times duplication [i] based on digital (94, 124, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 31, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(126−30, 126, 1621)-Net over F₄ — Digital

Digital (96, 126, 1621)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(126−30, 126, 244302)-Net in Base 4 — Upper bound on s

There is no (96, 126, 244303)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7237 210099 361369 677874 556743 240567 922880 734711 201601 183714 209231 148269 569884 > 4¹²⁶ [i]