MinT - Best Known (102, 102+31, s)-Nets in Base 4

Best Known (102, 102+31, s)-Nets in Base 4

(102, 102+31, 1036)-Net over F₄ — Constructive and digital

Digital (102, 133, 1036)-net over F₄, using

4¹ times duplication [i] based on digital (101, 132, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 33, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(102, 102+31, 1889)-Net over F₄ — Digital

Digital (102, 133, 1889)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 102+31, 425364)-Net in Base 4 — Upper bound on s

There is no (102, 133, 425365)-net in base 4, because

1 times m-reduction [i] would yield (102, 132, 425365)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 29 643485 586280 691665 464711 977911 814907 021893 116948 719619 996925 321268 918055 223440 > 4¹³² [i]