MinT - Best Known (233−57, 233, s)-Nets in Base 4

Best Known (233−57, 233, s)-Nets in Base 4

(233−57, 233, 1032)-Net over F₄ — Constructive and digital

Digital (176, 233, 1032)-net over F₄, using

4¹ times duplication [i] based on digital (175, 232, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 58, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(233−57, 233, 2343)-Net over F₄ — Digital

Digital (176, 233, 2343)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(233−57, 233, 366736)-Net in Base 4 — Upper bound on s

There is no (176, 233, 366737)-net in base 4, because

1 times m-reduction [i] would yield (176, 232, 366737)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47 636929 350826 317308 683771 201160 552079 049691 667380 095655 326193 932394 939242 052943 464717 579811 654686 048374 069498 339680 298045 070145 858374 012128 > 4²³² [i]