MinT - Best Known (123−29, 123, s)-Nets in Base 4

Best Known (123−29, 123, s)-Nets in Base 4

(123−29, 123, 1032)-Net over F₄ — Constructive and digital

Digital (94, 123, 1032)-net over F₄, using

1 times m-reduction [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]

(123−29, 123, 1676)-Net over F₄ — Digital

Digital (94, 123, 1676)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−29, 123, 355504)-Net in Base 4 — Upper bound on s

There is no (94, 123, 355505)-net in base 4, because

1 times m-reduction [i] would yield (94, 122, 355505)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 28 269633 301376 001299 541853 761197 187609 271052 210751 185019 490226 574962 049736 > 4¹²² [i]