MinT - Best Known (124, 161, s)-Nets in Base 4

Best Known (124, 161, s)-Nets in Base 4

(124, 161, 1040)-Net over F₄ — Constructive and digital

Digital (124, 161, 1040)-net over F₄, using

4¹ times duplication [i] based on digital (123, 160, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 40, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(124, 161, 2363)-Net over F₄ — Digital

Digital (124, 161, 2363)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 161, 565772)-Net in Base 4 — Upper bound on s

There is no (124, 161, 565773)-net in base 4, because

1 times m-reduction [i] would yield (124, 160, 565773)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 136002 872422 478010 425496 962431 240547 411292 218457 838770 309687 659202 262317 558311 717358 390678 221120 > 4¹⁶⁰ [i]