MinT - Best Known (97−32, 97, s)-Nets in Base 4

Best Known (97−32, 97, s)-Nets in Base 4

(97−32, 97, 195)-Net over F₄ — Constructive and digital

Digital (65, 97, 195)-net over F₄, using

4¹ times duplication [i] based on digital (64, 96, 195)-net over F₄, using
- trace code for nets [i] based on digital (0, 32, 65)-net over F₆₄, using
  - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
      - the rational function field F₆₄(x) [i]
    - Niederreiter sequence [i]

(97−32, 97, 319)-Net over F₄ — Digital

Digital (65, 97, 319)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−32, 97, 10112)-Net in Base 4 — Upper bound on s

There is no (65, 97, 10113)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 25130 929224 774576 332365 402498 201531 153769 356311 324219 610120 > 4⁹⁷ [i]