MinT - Best Known (131−31, 131, s)-Nets in Base 4

Best Known (131−31, 131, s)-Nets in Base 4

(131−31, 131, 1032)-Net over F₄ — Constructive and digital

Digital (100, 131, 1032)-net over F₄, using

1 times m-reduction [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]

(131−31, 131, 1723)-Net over F₄ — Digital

Digital (100, 131, 1723)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−31, 131, 353576)-Net in Base 4 — Upper bound on s

There is no (100, 131, 353577)-net in base 4, because

1 times m-reduction [i] would yield (100, 130, 353577)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 852679 919285 826850 164357 956333 899044 298648 230382 004796 665510 063741 470132 223904 > 4¹³⁰ [i]