MinT - Best Known (133−32, 133, s)-Nets in Base 4

Best Known (133−32, 133, s)-Nets in Base 4

(133−32, 133, 1032)-Net over F₄ — Constructive and digital

Digital (101, 133, 1032)-net over F₄, using

4¹ times duplication [i] based on digital (100, 132, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 33, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(133−32, 133, 1600)-Net over F₄ — Digital

Digital (101, 133, 1600)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−32, 133, 229095)-Net in Base 4 — Upper bound on s

There is no (101, 133, 229096)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 118 574093 820613 554313 987039 306650 349371 330334 626389 023745 412376 513211 678787 627874 > 4¹³³ [i]