MinT - Best Known (147−47, 147, s)-Nets in Base 4

Best Known (147−47, 147, s)-Nets in Base 4

(147−47, 147, 240)-Net over F₄ — Constructive and digital

Digital (100, 147, 240)-net over F₄, using

t-expansion [i] based on digital (99, 147, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 49, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(147−47, 147, 497)-Net over F₄ — Digital

Digital (100, 147, 497)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−47, 147, 20831)-Net in Base 4 — Upper bound on s

There is no (100, 147, 20832)-net in base 4, because

1 times m-reduction [i] would yield (100, 146, 20832)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7962 511760 925896 518737 431787 617712 008503 897305 278327 909626 560928 543438 246146 143447 639647 > 4¹⁴⁶ [i]